Syllabus of Mathematics

(For National and International Round)

Kindergarten  (Category 1)

• Addition and Subtraction – 1-digit numbers without carrying.
• Patterns and Sequences – Basic number and figure patterns.
• Counting and Recognition – Odd and even numbers, arranging numbers in order.
• Shapes – Identifying 2-D and 3-D shapes, counting sides and interior angles.
• Comparing Numbers – Greater, lesser, and equal to.
• Number Creation – Forming 3-digit numbers.
• Basic Equations – Simple matching equations.
• Balance Problems – Understanding equality in math.

Grades 1 – 2 (Category 2)

• Addition and Subtraction – 2-digit numbers with carrying.
• Patterns and Sequences – Number patterns, arithmetic sequences.
• Shapes – Counting sides and angles of 2D shapes, recognizing 3D shapes.
• Odd and Even Numbers
• Date and Age Problems
• Number Formation – 3-digit numbers.
• Basic Arithmetic Patterns – Recognizing and continuing patterns.
• Simple Combinations – Early combinatorics.
• Balance Problems

Grades 3 – 4 (Category 3)

• Addition and Subtraction – 3-digit numbers with carrying.
• Multiples and Factors – Sum, difference, multiples.
• Conceptual Problems – IQ age and date, Pigeonhole problem.
• Geometry – Area and perimeter basics, counting vertices, edges of 3D shapes.
• Basic Probability and Combinatorics – Early introduction.
• Routing Problems
• Basic LCM and HCF

Grades 5 – 6 (Category 4)

• Word Problems – Chicken and rabbit, speed and time, excess and shortage.
• Fractions and Decimals – Calculations involving decimal numbers.
• Geometry – Volume, surface area of 3D shapes, area/perimeter of 2D shapes.
• Series and Sums – Sum of positive numbers.
• Probability – Introductory probability concepts.
• Equations – Basic difference equations.
• Combinatorics – Combinations and permutations.
• 4-digit Numbers – Number guesswork.

Grades 7 – 8 (Category 5)

• Algebra – Expressions, inequalities, linear equations.
• Advanced Word Problems – Speed, distance, and time, harder pigeonhole problems.
• Advanced Geometry – Volume, surface area of complex shapes, Pythagorean Theorem.
• Probability – Intermediate probability concepts.
• Combinatorics – Permutations, counting solutions to indefinite equations.
• Factor Theorem
• Routing and Distribution Problems – Complex applications.

Grades 9 – 10 (Category 6)

• Number Theory – Operations on rational and irrational numbers, prime factorization.
• Word Problems – Real-world scenarios involving percentages, interest, and map scales.
• Algebra – Linear, quadratic expressions, remainder and factor theorems.
• Geometry and Trigonometry – Advanced shapes, angles, perimeter, volume, Pythagorean Theorem.
• Probability – Single events, advanced probability.
• Sequences and Patterns – Arithmetic progression, counting problems.
• Calculus – Introductory derivatives and integrals.
• Graphs – Understanding and interpreting various types of graphs.

Grades 11 – 12 (Category 7)

• Algebra – Advanced expressions, modulus functions, quadratic and cubic equations.
• Graphs and Functions – Power functions, trigonometric identities, sine, cosine graphs.
• Geometry – Advanced concepts in circles, similarity, congruence, and 3D trigonometry.
• Probability – Combined events, tree diagrams, possibility diagrams.
• Sequences and Patterns – Arithmetic progression, terminal zeros, and divisibility.
• Advanced Calculus – Logarithmic laws, derivatives, integrals.
• Logic and Cryptarithms – Puzzles and advanced problem-solving.
• Coordinate Geometry – Gradient, line segment lengths, and shoelace formula.